I think I've got the general idea, I'm just a bit confused on the instructions.

For one color, the instructions read "k1 MC, p1 CC" and then for the next color, it says "k1 CC, p1 MC"

Do I do the instructions in that order, or do I do it based on the color?
For instance, I have my CC on my needle as the first stitch, but the instructions say to k1 MC. So, do I knit my main color then, or do I wait for the next main-colored stitch on my needle?

I'm sorry this is a bit confusing. If you have questions on what I'm trying to say, I'll try to draw something on paint.

I think the chart directions with the K1 MC, P1 CC color etc. are for doing double knitting. That is where you are knitting two layers at once. I don't know much about double knitting, if you really want to do double knitting send a private message to Of Troy, she is our resident expert on double knitting.

If you just want to use that chart to do a design like that in regular knitting just knit each stitch once in the color you see on the chart. If you are knitting back and forth remember that that the knit rows are worked right to left and on the purl rows you read the chart from left to right, and of course you would purl back if you are doing stockinette. If you are working in the round you read all rows right to left.

The chart looks as though you don't have to mentally switch colors, so you just do it as the chart shows it. I suppose you know that you are double knitting.

If the square on the chart is grey, you knit with MC, then purl the next (corresponding) stitch with CC, if the chart shows green square, you knit with the CC, then purl with the MC.

(Normally, you have to switch colors of chart from one row to the next, so even if it said "green square" on the chart, you would do "grey square" instead. But this chart doesn't seem that way, which is less confusing.)